Now showing 1 - 10 of 10
  • Publication
    Lassoing the HAR model: A Model Selection Perspective on Realized Volatility Dynamics
    (Taylor & Francis, 2014-06-13) ;
    Knaus, Simon
    Realized volatility computed from high-frequency data is an important measure for many applications in finance and its dynamics have been widely investigated. Recent notable advances that perform well include the heterogeneous autoregressive (HAR) model which can approximate long memory, is very parsimonious, is easy to estimate, and features good out-of-sample performance. We prove that the least absolute shrinkage and selection operator (lasso) recovers the lags structure of the HAR model asymptotically if it is the true model, and we present Monte Carlo evidence in finite samples. The HAR model's lags structure is not fully in agreement with the one found using the lasso on real data. Moreover, we provide empirical evidence that there are two clear breaks in structure for most of the assets we consider. These results bring into question the appropriateness of the HAR model for realized volatility. Finally, in an out-of-sample analysis we show equal performance of the HAR model and the lasso approach.
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  • Publication
    Measuring spot variance spillovers when (co)variances are time-varying - the case of multivariate GARCH models
    ( 2015) ;
    Herwartz, Helmut
    In highly integrated markets, news spreads at a fast pace and bedevils risk monitoring and optimal asset allocation. We therefore propose global and dis- aggregated measures of variance transmission that allow one to assess spillovers locally in time. Key to our approach is the vector ARMA representation of the second-order dynamics of the popular BEKK model. In an empirical applica- tion to a four-dimensional system of US asset classes - equity, fixed income, foreign exchange and commodities - we illustrate the second-order transmis- sions at various levels of (dis)aggregation. Moreover, we demonstrate that the proposed spillover indices are informative on the value-at-risk violations of port- folios composed of the considered asset classes.
  • Publication
    Lassoing the HAR model: A Model Selection Perspective on Realized Volatility Dynamics
    (SEPS, 2012) ;
    Knaus, Simon
    Realized volatility computed from high-frequency data is an important measure for many applications in finance. However, its dynamics are not well understood to date. Recent notable advances that perform well include the heterogeneous autoregressive (HAR) model which is economically interpretable and but still easy to estimate. It also features good out-of-sample performance and has been extremely well received by the research community. We present a data driven approach based on the absolute shrinkage and selection operator (lasso) which should identify the aforementioned model. We prove that the lasso indeed recovers the HAR model asymptotically if it is the true model, and we present Monte Carlo evidence in finite sample. The HAR model is not recovered by the lasso on real data. This, together with an empirical out-of-sample analysis that shows equal performance of the HAR model and the lasso approach, leads to the conclusion that the HAR model may not be the true model but it captures a linear footprint of the true volatility dynamics.
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  • Publication
    Testing the lag structure of assets' realized volatility dynamics
    (SEPS Discussion Paper Series, 2015) ;
    Camponovo, Lorenzo
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    Roth, Constantin
    A (conservative) test is constructed to investigate the optimal lag structure for forecasting realized volatility dynamics. The testing procedure relies on the recent theoretical results that show the ability of the adaptive least absolute shrinkage and selection operator (adaptive lasso) to combine efficient parameter estimation, variable selection, and valid inference for time series processes. In an application to several constituents of the S\&P 500 index it is shown that (i) the optimal significant lag structure is time-varying and subject to drastic regime shifts that seem to happen across assets simultaneously; (ii) in many cases the relevant information for prediction is included in the first 22 lags, corroborating previous results concerning the accuracy and the difficulty of outperforming out-of-sample the heterogeneous autoregressive (HAR) model; and (iii) some common features of the optimal lag structure can be identified across assets belonging to the same market segment or showing a similar beta with respect to the market index.
  • Publication
    Global Equity Market Volatility Spillovers: A Broader Role for the United States
    (SEPS, 2015) ;
    Gisler, Katja
    Rapach et al. (2013) have recently shown that U.S. equity market returns carry valuable information to improve return forecasts in a large cross-section of international equity mar- kets. In this study, we extend the work of Rapach et al. (2013) and examine if U.S. based eq- uity market information can be used to improve realized volatility forecasts in international equity markets. For that purpose, we obtain volatility data for the U.S. and 17 international equity markets from the Oxford Man Institute's realized library and augment for each for- eign equity market the benchmark HAR model with lagged U.S. equity market volatility information. In-sample as well as out-of-sample evaluation results suggest a strong role for U.S. based volatility information. More specifically, apart from standard in-sample tests, which find U.S. volatility information to be highly significant, we show that this information can be used to substantially improve out-of-sample forecasts of realized volatility. Using large out-of-sample evaluation periods containing at least 2500 observations, we find that forecast improvements, as measured by the out-of-sample R2 (relative to a model that does not include U.S. based volatility information), can be as high as 12.83, 10.43 and 9.41 percent for the All Ordinaries, the Euro STOXX 50 and the CAC 40 at the one-step-ahead horizon. Moreover, forecast improvements are highly significant at the one-step-ahead horizon for all 17 equity markets that we consider, yielding Clark-West adjusted t ? statistics of over 7. We show further that the improvements from including U.S. based volatility information are consistently experienced over the entire out-of-sample period that we consider, and hold for forecast horizons of up to 22 days ahead.
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  • Publication
    Specification and structural break tests for additive models with applications to realized variance data
    (Elsevier, 2015-09-01) ;
    Mammen, Enno
    ;
    Vogt, Michael
    We study two types of testing problems in a nonparametric additive model setting: We develop methods to test (i) whether an additive component function has a given parametric form and (ii) whether an additive component has a structural break. We apply the theory to a nonparametric extension of the linear heterogeneous autoregressive model which is widely employed to describe realized variance data. We find that the linearity assumption is often rejected, but actual deviations from linearity are mild.
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    Scopus© Citations 8
  • Publication
    A variance spillover analysis without covariances: what do we miss?
    (Elsevier, 2015-03-01) ;
    Gisler, Katja
    We evaluate the relevance of covariances in the transmission mechanism of variance spillovers across the US stock, US bond and gold markets from July 2003 to December 2012. For that purpose, we perform a comparative spillover analysis between a model that considers covariances and a model that considers only variances. Our results emphasise the importance of covariances. Including covariances leads to an overall increase of the spillover level and detects the beginnings of the financial crisis and of the US debt ceiling crisis earlier than the spillover measure that considers only variances. Even for the low-dimensional system that we consider, one misses important variance spillover channels when covariances are excluded.
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    Scopus© Citations 63
  • Publication
    Volatility Forecasting: Downside Risk, Jumps and Leverage Effect
    (MDPI, 2016-02-23) ;
    Hu, Yujia
    We provide empirical evidence on volatility forecasting in relation to asymmetries present in the dynamics of both return and volatility processes. Using recently developed methodologies to detect jumps from high frequency price data, we estimate the size of positive and negative jumps and propose a methodology to estimate the size of jumps in the quadratic variation. The leverage effect is separated into continuous and discontinuous effects and past volatility is separated into ``good" and ``bad" as well as into continuous and discontinuous risks. Using a long history of the S\&P500 price index, we find that the continuous leverage effect lasts about one week while the discontinuous leverage effect disappears after one day. ``Good" and ``bad" continuous risks both characterize the volatility persistence while ``bad" jump risk is much more informative than ``good" jump risk in forecasting future volatility. The volatility forecasting model proposed is able to capture many empirical stylized facts while still remaining parsimonious in terms of the number of parameters to be estimated.
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    Scopus© Citations 39
  • Publication
    Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation
    (Wiley-Blackwell, 2015-05-01)
    Corsi, Fulvio
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    Peluso, Stefano
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    Motivated by the need of a positive-semidefinite estimator of multivariate realized covariance matrices, we model noisy and asynchronous ultra-high-frequency asset prices in a state-space framework with missing data. We then estimate the covariance matrix of the latent states through a Kalman smoother and Expectation Maximization (KEM) algorithm. Iterating between the two EM steps, we obtain a covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive-semidefinite by construction. We show the performance of the KEM estimator using extensive Monte Carlo simulations that mimic the liquidity and market microstructure characteristics of the S&P 500 universe as well as in an high-dimensional application on US stocks. KEM provides very accurate covariance matrix estimates and significantly outperforms alternative approaches recently introduced in the literature.
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    Scopus© Citations 29
  • Publication
    Managing Risk with a Realized Copula Parameter
    (Elsevier, 2016-08) ;
    Okhrin, Ostap
    A dynamic copula model is introduced, in which the copula structure is inferred from the realized covariance matrix estimated from within-day high-frequency data. The estimation is carried out in a method-of-moments fashion using Hoeding's lemma. Applying this procedure day by day gives rise to a time series of daily copula parameters which can be approximated by an autoregressive time series model. This allows one to capture time-varying dependence. In an application to portfolio risk-management, it is found that this time-varying realized copula model exhibits very good forecasting properties for the one-day ahead value at risk. The working paper version of this paper ("Realized Copula") is found on http://www1.vwa.unisg.ch/RePEc/usg/econwp/EWP-1214.pdf
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    Scopus© Citations 17